The model (REF ) have been studied in literature[1]}, and it was known that there are several magnetically ordered phases in the ground state phase diagram. In mean field theory, the magnetically ordered states are essentially the same as the classical ground states whose energy can be easily calculated[2]}. Therefore, we will focus on possible QSL phases. Noticing that the pure Kitaev model is a special point in the model (REF ), it is expected that the phase diagram contains at least one QSL phase, the Kitaev Spin Liquid (KSL) phase. In the following we will investigate if there exist other QSL phases.
